For a rigid body to be in equilibrium, two conditions must be met: the sum of all external forces acting on the body must be zero, and the sum of all external torques acting on the body must also be zero.
A rigid body will remain in equilibrium when acted upon by a non-parallel coplanar force if the vector sum of all forces acting on the body is zero, and the vector sum of all torques (or moments) acting on the body is also zero. This condition is known as the equilibrium of forces and moments.
Force couples create a turning effect on a rigid body without causing any translation. This affects the stability and equilibrium of the body by creating a moment that counteracts other external forces, helping to maintain balance and prevent rotation.
For two bodies in physical contact to remain in equilibrium, the condition necessary is that the sum of the forces acting on each body must be equal and opposite.
Rest refers to a state of inactivity or lack of motion, while equilibrium is the state of balance in which opposing forces or influences are balanced. Rest is a specific condition where an object is stationary, while equilibrium refers to a broader concept of balance between different factors.
For a body to be in equilibrium, the net force acting on it must be zero, meaning that the forces in all directions are balanced. Additionally, the net torque (or rotational force) acting on the body must also be zero, ensuring that it is not rotating.
A rigid body will remain in equilibrium when acted upon by a non-parallel coplanar force if the vector sum of all forces acting on the body is zero, and the vector sum of all torques (or moments) acting on the body is also zero. This condition is known as the equilibrium of forces and moments.
equilbrium in coplaner forces at rigid body.
Consider two equal and opposite forces acting along different lines of the body, which causes the body to rotate, although first condition is fulfilled but body is still moving. Thus, we need another condition for equilibrium that is the second condition of equilibrium.
The equilibrium condition requires the sum of the forces on the body to be zero.
The principle of transmissibily states that the the conditions of equilibrium(uniform mothion) of a rigid body will remain unchanged if a force acting at a given point of the rigid body is tansmitted along its line of action to another point with the same magnitude and same direction.
first condition for equilibrium is that the a body is satisfy with first condition if the resultant of all the forces acting on it is zero let n numbers of the forces F1, F2,F3,.........., Fn are acting on a body such that sigmaF=0 a book lying on a table or picture hanging on the wall are at rest and thus satisfy with first condition of equilibrium a paratrooper coming with terminal velocity also satisfies first condition of equilibrium
The first condition of equilibrium can be applied on concurrent forces that are equal in magnitude, since these produce translational equilibrium. But if the forces are equal in magnitude but are non concurrent then even first condition of equilibrium is satisfied but torque is produced which does not maintain rotational equilibrium. Hence for complete equilibrium that is, both translational and rotational , both the conditions should be satisfied.
A rigid body will have a natural frequency of vibration due to its mass and stiffness properties. When disturbed from its equilibrium position, the body will oscillate at this natural frequency. This frequency is determined by the body's physical characteristics and can be calculated using principles of dynamics.
Force couples create a turning effect on a rigid body without causing any translation. This affects the stability and equilibrium of the body by creating a moment that counteracts other external forces, helping to maintain balance and prevent rotation.
In statics a particle and a rigid body are viewed as pretty much the same thing, and can be analysed with the same methods. Assuming that a particle is in equilibrium i.e. the sum of the forces and the moments are all zero, and that a rigid body is made up of particles, we know that if each particle of this body is in equilibrium (internal forces cancel each other out) then we can conclude that the body must therefore also be in equilibrium. The difference between these a particle and a body is we will usually find a particle in space without these so-called constraints, while a rigid body- a beam comes immediately to mind, is usually constrained in some or other manner, by either a pin or roller or any other way.
In classical physics, a rigid body is an idealization where the distance between any two points on the body remains constant. However, in reality, all physical bodies have some degree of flexibility or deformation under certain conditions. Therefore, there is no truly rigid body in practice.
When a body or a system is in equilibrium, there is no net tendency to change. Everything is equal.